Balance Laws and Constitutive Relations for Plane Flows of a Dense, Binary Mixture of Smooth, Nearly Elastic, Circular Disks

1987 ◽  
Vol 54 (1) ◽  
pp. 27-34 ◽  
Author(s):  
J. T. Jenkins ◽  
F. Mancini
Keyword(s):  
Distribution Function ◽  
Binary Mixture ◽  
Pair Distribution Function ◽  
Constitutive Relations ◽  
Balance Laws ◽  
Focus Attention ◽  
Circular Disks

We derive balance laws and constitutive relations for plane flows of a dense, binary mixture of smooth, nearly elastic, circular disks. The disks may differ in size and mass and in the coefficients of restitution characterizing the energy lost in collisions between like and unlike pairs. We focus attention on those parts of the fluxes and sources of momentum and energy that are due to collisions. To calculate them, we suppose that the complete pair distribution function for two colliding disks is the product of Maxwellian velocity distributions for each disk and a factor that incorporates the effects of excluded area and collisional shielding. In an Appendix we provide constitutive relations calculated in a similar way for a dense, binary mixture of smooth, nearly elastic, spheres.

The Thickness of Steady Plane Shear Flows of Circular Disks Driven by Identical Boundaries

1988 ◽  
Vol 55 (4) ◽  
pp. 969-974 ◽  
Author(s):  
D. M. Hanes ◽  
J. T. Jenkins ◽  
M. W. Richman
Keyword(s):  
Relative Motion ◽  
Constitutive Relations ◽  
Balance Laws ◽  
Plane Shear ◽  
Normal Traction ◽  
Steady Solutions ◽  
Steady Shearing ◽  
Steady Plane ◽  
Steady Motions ◽  
Circular Disks

We employ balance laws and constitutive relations for rapid, dense, plane flows of identical circular disks together with boundary conditions at a bumpy wall to analyse steady shearing flows maintained by the relative motion of two identical, parallel walls. The disks and the walls are assumed to be frictionless and nearly elastic. Given the properties of the flowing disks, those of the boundary, and the ratio of the tangential and normal tractions applied to the boundary, we determine what the distance between the walls must be for a steady solution to be possible. For these steady solutions we relate the velocity of the walls to the normal and tangential tractions applied to them. We find that in certain circumstances steady motions may be maintained even when the ratio of tangential to normal traction is much less than its value in a homogeneous simple shear. In the Appendix, the corresponding results for spheres are outlined.

Real-Space X-Ray Pair Distribution Function Analysis and Molecular-Dynamics Modelling of Diflunisal Channel Hydrates

2020 ◽  
Author(s):  
Anuradha Pallipurath ◽  
Francesco Civati ◽  
Jonathan Skelton ◽  
Dean Keeble ◽  
Clare Crowley ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Distribution Function ◽  
Structural Dynamics ◽  
First Principles ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Real Space ◽  
X Ray ◽  
Dynamics Modelling ◽  
Dynamics Simulations

X-ray pair distribution function analysis is used with first-principles molecular dynamics simulations to study the co-operative H<sub>2</sub>O binding, structural dynamics and host-guest interactions in the channel hydrate of diflunisal.

Engineering Porosity Through Defects in a Giant Pore Metal–Organic Framework

2020 ◽  
Author(s):  
Adam Sapnik ◽  
Duncan Johnstone ◽  
Sean M. Collins ◽  
Giorgio Divitini ◽  
Alice Bumstead ◽  
...  
Keyword(s):  
Distribution Function ◽  
Ball Milling ◽  
Local Structure ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Metal Organic Framework ◽  
Metal Organic Frameworks ◽  
Defect Engineering ◽  
Metal Organic ◽  
Unsaturated Metal Sites

<p>Defect engineering is a powerful tool that can be used to tailor the properties of metal–organic frameworks (MOFs). Here, we incorporate defects through ball milling to systematically vary the porosity of the giant pore MOF, MIL-100 (Fe). We show that milling leads to the breaking of metal–linker bonds, generating more coordinatively unsaturated metal sites, and ultimately causes amorphisation. Pair distribution function analysis shows the hierarchical local structure is partially</p><p>retained, even in the amorphised material. We find that the solvent toluene stabilises the MIL-100 (Fe) framework against collapse and leads to a substantial rentention of porosity over the non-stabilised material.</p>

scholarly journals Crystal Structure of Moganite and Its Anisotropic Atomic Displacement Parameters Determined by Synchrotron X-ray Diffraction and X-ray/Neutron Pair Distribution Function Analyses

Minerals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 272
Author(s):  
Seungyeol Lee ◽  
Huifang Xu ◽  
Hongwu Xu ◽  
Joerg Neuefeind
Keyword(s):  
Crystal Structure ◽  
Distribution Function ◽  
Single Crystal ◽  
Pair Distribution Function ◽  
Atomic Displacement ◽  
Single Crystal Xrd ◽  
X Ray Diffraction ◽  
X Ray ◽  
Neutron Pair ◽  
Atomic Displacement Parameters

The crystal structure of moganite from the Mogán formation on Gran Canaria has been re-investigated using high-resolution synchrotron X-ray diffraction (XRD) and X-ray/neutron pair distribution function (PDF) analyses. Our study for the first time reports the anisotropic atomic displacement parameters (ADPs) of a natural moganite. Rietveld analysis of synchrotron XRD data determined the crystal structure of moganite with the space group I2/a. The refined unit-cell parameters are a = 8.7363(8), b = 4.8688(5), c = 10.7203(9) Å, and β = 90.212(4)°. The ADPs of Si and O in moganite were obtained from X-ray and neutron PDF analyses. The shapes and orientations of the anisotropic ellipsoids determined from X-ray and neutron measurements are similar. The anisotropic ellipsoids for O extend along planes perpendicular to the Si-Si axis of corner-sharing SiO4 tetrahedra, suggesting precession-like movement. Neutron PDF result confirms the occurrence of OH over some of the tetrahedral sites. We postulate that moganite nanomineral is stable with respect to quartz in hypersaline water. The ADPs of moganite show a similar trend as those of quartz determined by single-crystal XRD. In short, the combined methods can provide high-quality structural parameters of moganite nanomineral, including its ADPs and extra OH position at the surface. This approach can be used as an alternative means for solving the structures of crystals that are not large enough for single-crystal XRD measurements, such as fine-grained and nanocrystalline minerals formed in various geological environments.

In situ pair distribution function analysis of crystallizing Fe-silicate melts

2021 ◽  
Vol 56 (9) ◽  
pp. 5637-5657
Author(s):  
Emily T. Nienhuis ◽  
Manzila Tuheen ◽  
Jincheng Du ◽  
John S. McCloy
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Silicate Melts
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